This dissertation presents a novel multiscale computational framework for simulating failure and damage accumulation in brittle composites. A reduced-order multiple spatial scale methodology is developed to efficiently model failure under monotonic loading conditions. This methodology is based on the computational homogenization approach. The proposed reduced order approach is computationally efficient when compared to standard computational homogenization. Modeling of individual failure modes, such as matrix cracking, matrix/fiber debonding, delamination, and fiber fracture are incorporated into this methodology. A multiple spatio-temporal scale technique is proposed for simulating failure in composites subjected to cyclic loading conditions. This technique is based on the generalization of the homogenization approach to temporal scales. An adaptive macrochronological time stepping algorithm is devised to predict damage accumulation by resolving a small subset of cycles throughout the life of the composite. The proposed multiscale framework was verified by numerical simulation and was validated using experimental testing. Experimental validation involved a series of monotonic and fatigue experiments conducted on the carbon fiber reinforced polymer composite, IM7/977-3. Non-destructive inspection techniques including acoustic emission, X-ray radiography, and X-ray computed tomography were utilized to characterize progressive damage accumulation in the composite material. The multiple spatio-temporal model was calibrated and employed to predict the failure response of IM7/977-3 specimens. The proposed model was demonstrated to accurately and efficiently predict strength, ductility, and damage growth characteristics under both monotonic and cyclic loadings. The combined computational and experimental investigation provided a thorough picture of the failure processes of this material.

Multiple sources of errors and uncertainty arise in mechanics computational models and contribute to the error and uncertainty in the final model prediction. This research develops a systematic error quantification methodology for computational models. Some types of errors are deterministic, and some are stochastic. Appropriate procedures are developed to either correct the model prediction for deterministic errors or to account for the stochastic errors through sampling. First, input error, discretization error in FEA, surrogate model error, and output measurement error are considered. Next, uncertainty quantification error which arises due to the use of sampling-based methods is also investigated. Model form error is estimated based on the comparison of corrected model prediction against physical observations, and after accounting for solution approximation errors, uncertainty quantification errors, and experimental errors (input and output). Both local and global sensitivity measures are investigated to estimate and rank the contribution of each source of error to the uncertainty in the final result. Two numerical examples are used to demonstrate the proposed methodology, by considering mechanical stress analysis and fatigue crack growth analysis.

Composites and adhesive joints are being increasingly used in modern structures. It becomes very important to characterize the failure in such materials especially at the interface between constituents. This dissertation is focused on interfacial failure in composites and bonded polymers. A short-beam shear fracture approach is developed to measure the mode-II fracture toughness of materials with a preferred interface. This method is more efficient than previous methods due to minimal friction between crack faces. A novel failure criterion proposed by Leguillon (2002) is used to predict crack initiation from notches. This dissertation advances the scope of this criterion to predict failure from notches with a connected interface. Same- and bi-material systems are tested under three-point bending to provide relevant data for verification which is also expected to be a benchmark for future numerical simulations. Finally, the compression-after-impact (CAI) of glass/vinyl ester composites subject to sea water aging is investigated experimentally. A reduced order multiscale computational model is used to explain the damage mechanisms in the composite and to capture the experimental degradation in CAI strength.

Many of the steel and concrete bridges built in the 20th century are reaching the end of their planned service life in the early part of the new century. Corrosion and fatigue fracture of steel, and cracking, spalling, or delamination of concrete are common deteriorations due to harsh environments. The structural deficiency of these bridges is further aggravated by heavier and faster traffic loads than what they were originally designed. Effective life management of the large number of deficient and/or obsolete bridges with limited budgets requires post-strengthening, retrofitting, or repair, with minimum interference of traffic and cost. In some cases, localized repair can extend the life for a period of time using a repair method based on bonded fiber-reinforced polymers (FRP) patches for both steel and concrete bridges. This repair solution may prove effective for excessive flexural and shear cracks in concrete beams, and section loss of steel beams.This thesis is concerned with predicting the performance of such patch repaired beams using mechanistic modeling and experimental testing. Steel, reinforced concrete, and prestressed concrete beams test beams are utilized and the predicted response values are compared and validated.

Roadway closures due to highway incidents are detrimental to the American economy and result in lost time for motorists. Route diversion can help lessen the effects of highway incidents, if the decision is based upon a set of criteria that helps evaluate the impacts of the rerouted traffic. These criteria must meet two conditions: 1) quantifiable and 2) can be evaluated in a time-efficient manner. Based on a review of existing routing methods, criteria were defined according to three key considerations: 1) geometric characteristics, 2) proximity, and 3) capacity. Performance measures for these criteria were determined and applied to the Tennessee interstate highway network by utilizing GIS software to determine incident hot spots worthy of rerouting consideration. The application of the criteria led to diversion route selections that minimized travel time, while satisfying truck operational constraints, and maintaining an acceptable level of service (LOS) when additional traffic was assigned to the route. The methodology described in this document can be applied to roadway networks in other locations in order to facilitate diversion decisions. The research presented can also be used as a basis for developing more enhanced tools for making more efficient rerouting decisions while maintaining operational safety.

This dissertation develops a general methodology for probabilistic prediction of railroad wheel failure life considering uncertainties from several possible sources. The two most dominant failure types, shattered rim and vertical split rim failures, occurring due to sub-surface crack propagation, are considered. The crack modeling uses 3-D finite element analysis and linear elastic fracture mechanics. For computational efficiency, the finite element analysis is divided into two stages: full model analysis and sub-model analysis. In the full model analysis, complete wheel geometry is considered and rolling contact analysis is performed. In the sub-model analysis, a small block with an embedded 3D fatigue crack is considered and elastic-plastic analysis is performed by applying full model results as boundary conditions. A mixed-mode crack model based on critical plane concepts is used to compute the equivalent stress intensity factor range (Keq) at the crack tip using the uni-modal values obtained from the finite element analysis. Variable amplitude loading, multi-axial fatigue, residual stresses (both as-manufactured and service-induced), and wheel wear are included in the analysis. Residual stresses in the wheel rim can affect Keq at sub-surface crack tips, and thereby the wheel failure life. Therefore, residual stresses developed during both the manufacturing process and due to the thermal brake loading under service conditions, are estimated using three-dimensional decoupled thermal-structural finite element analyses, and these estimated results are included as initial stresses for rolling contact analysis. Wheel wear is assumed to be uniform for the sake of illustration. Since finite element analysis to estimate the Keq at a sub-surface crack tip for cycle-by-cycle calculations is computationally expensive, a Kriging-based meta-model is developed to represent the relationship between the input parameters and Keq at the crack tip. The uncertainties in various input parameters are considered through probabilistic analysis. Multiple sets of Monte Carlo simulations are performed to obtain the failure life probability distributions and the scatter in the computed results. The numerical results are validated using field data.

A comprehensive framework for the treatment of uncertainty is essential to facilitate decision-making in engineering systems at every stage of the life cycle, such as design, manufacturing/construction, operations, system health assessment and risk management. This dissertation advances the state of the art in uncertainty quantification methods by systematically accounting for the various sources of uncertainty (natural variability, data uncertainty, and model uncertainty) in order to compute the overall uncertainty in the system-level prediction. First, a likelihood-based methodology is developed in order to represent epistemic uncertainty (due to sparse/imprecise data) using probability distributions, thereby facilitating combined treatment of aleatory and epistemic uncertainty. Second, computational methods are developed to systematically include the various sources of uncertainty in model verification, validation and calibration activities. Third, a Bayesian network-based methodology is developed for integrating the results of various uncertainty quantification activities in hierarchical system models. Different types of hierarchical system models, including multi-physics and multi-level models, are considered. Fourth, the Bayesian methodology is used to guide decision-making with respect to test resource allocation for uncertainty quantification. Finally, a methodology for inverse sensitivity analysis is developed in order to analyze the effect of various sources of uncertainty on the variance of posterior estimation and thereby aid in design of experiments and dimension reduction. The proposed methods are applied to civil, mechanical, and aerospace structures.

Testing or performing inspections to gain information and reduce uncertainty is a necessary activity during the life-cycle of any engineering system. This study develops analytical methods for the optimization of test and inspection campaigns at various system levels in order to reduce the uncertainty of the full system model prediction. The Bayesian network methodology is utilized to connect models, uncertain quantities, testing or inspection data, and various errors in a unified framework so that gaining information at a lower level can be used to reduce the uncertainty of the full system output. Once the Bayesian network is established, different test campaign options can be compared. The testing campaign which is likely to provided data that most efficiently and effectively reduces the uncertainty in the full system output is chosen as optimal. Four methodologies are developed that solve different test selection problems for engineering systems: (1) test-type selection, (2) test input setting design, (3) test campaign design for manufacturing optimization, and (4) inspection type selection during system operation. These methodologies are demonstrated on various multi-physics, multi-scale aerospace application problems including, a thermal vibration problem, a simplified telescope mirror problem, and a fatigue crack growth problem.

The research described herein was performed in an effort to determine how federal transportation expenditures benefit the freight industry. This study focused on two objectives: 1) determining relevant federal investments on highway and waterway freight modes and 2) calculating investment efficiency for each of these modes. On this basis, the efficiency of each mode in terms of tons of freight moved per dollar of investment can be compared. This was accomplished using data collected from multiple transportation agencies and federal sources based on the availability of the most recent information. While it was determined that federal freight investment in waterways is more efficient than for highways, there are more factors to consider. This effort demonstrates the challenge of collecting and analyzing investment and performance data and highlights the ancillary benefits of investment in each transportation mode that must be considered in future investment decisions.

This dissertation develops a systematic and comprehensive approach to management of uncertainty by accomplishing four major objectives: address model uncertainty for the permanent deformation model, develop a method to reduce computational expense, design a framework for incorporation of uncertainty in pavement design, and demonstrate a framework for risk-based mechanistic-empirical (M-E) pavement design. Pavement analysis is impacted by uncertainty from a number of significant sources such as field variables, uncertainty in the predicted behavior models, and errors in these models. These sources of uncertainty are not currently accounted for in the pavement design process in an efficient and comprehensive way. Management of uncertainty for M-E pavement design requires quantification of model uncertainty and the permanent deformation model is significantly susceptible to model uncertainty. A thorough calibration process is performed in this dissertation on three prevalent permanent deformation models: a model incorporating shear theory, an axial strain model, and a model combining both mechanistic theories. Understanding the uncertainty associated with these permanent deformation models is necessary to accurately predict pavement performance, but current models are computationally expensive. A surrogate model is constructed that accurately emulates the M-E flexible pavement design equations. The third major objective develops a logical and efficient process for incorporating uncertainty into M-E pavement design. Propagation of uncertainty from input variability, M-E prediction models, and the surrogate model is demonstrated and a sensitivity analysis is performed. Analysis of methods for the selection of the quantity and location of training points for the surrogate model is presented. Reliability analysis is performed utilizing probabilistic and analytical methods. A method for developing load and resistance factors is presented as a practice-ready option for reliable pavement design. The final major objective presents a framework for risk-based design in the context of mechanistic-empirical pavement design. Through these four major objectives, this dissertation presents a comprehensive framework for management of uncertainty in flexible pavement design.